We study the efficiency of the magnetoimpedance (MI) of thin-walled circumferentially-ordered nanotubes in sub-GHz and GHz frequency regimes, using micromagnetic simulations. We consider empty ferromagnetic tubes as well as tubes filled with non-magnetic conductors of circular cross-section (nanowire coverings), focusing on the low-field regime of MI (below a characteristic field of the low-frequency ferromagnetic resonance). In this field area, the efficient mechanism of MI is related to oscillations of the positions of (perpendicular to the tube axis) domain walls (DWs). Two mechanisms of driving the DW motion with the AC current are taken into account; the driving via the Oersted field and via the spin-transfer torque. The simulations are performed for Co nanotubes of the diameter of 300nm. Achievable low-field MI exceeds 100%, while the field region of a high sensitivity of that DW-based giant MI is of the width of tens of kA/m. The later is widely adjustable with changing the density of the driving AC current, its frequency, and the nanotube length. Of particular interest is the resonant motion of DW due to the interaction with the nanotube ends, the conditions of whom are discussed.

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